Critical properties of a one-dimensional nonlinear lattice and hadron physics

The statistical properties of a one-dimensional system are studied in the Ginzburg-Landau framework, where the most general free-energy density allowing for scale invariance is introduced. The grand partition function is expressed as a functional integral over the order-parameter function space and leads to an analytically soluble model. Near the critical point only the constant functions contribute to the thermodynamic potential, the system is simulated by a classical nonlinear lattice, and Kadanoff scaling is shown to be equivalent to Koba-Nielsen-Olesen scaling. The relevance of this lattice to hadron physics is established and several measurable quantities, such as multiplicities and correlations, are calculated. It is argued that, in the framework of this model, certain aspects of observable quantities could naturally be attributed to the past hadronization transition of a quark-gluon plasma